Answer :
To solve for [tex]\((f - g)(2)\)[/tex], we need to understand that this expression represents the difference between the functions [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex] evaluated at [tex]\(x = 2\)[/tex].
1. Evaluate [tex]\(f(x)\)[/tex] at [tex]\(x = 2\)[/tex]:
Recall the function [tex]\(f(x) = 3x^2 + 1\)[/tex].
Plug in [tex]\(x = 2\)[/tex]:
[tex]\[ f(2) = 3(2)^2 + 1 \][/tex]
Calculate the square of 2:
[tex]\[ (2)^2 = 4 \][/tex]
Multiply by 3:
[tex]\[ 3 \times 4 = 12 \][/tex]
Add 1:
[tex]\[ 12 + 1 = 13 \][/tex]
Therefore,
[tex]\[ f(2) = 13 \][/tex]
2. Evaluate [tex]\(g(x)\)[/tex] at [tex]\(x = 2\)[/tex]:
Recall the function [tex]\(g(x) = 1 - x\)[/tex].
Plug in [tex]\(x = 2\)[/tex]:
[tex]\[ g(2) = 1 - 2 \][/tex]
Subtract 2 from 1:
[tex]\[ 1 - 2 = -1 \][/tex]
Therefore,
[tex]\[ g(2) = -1 \][/tex]
3. Combine the results to find [tex]\((f - g)(2)\)[/tex]:
The expression [tex]\((f - g)(2)\)[/tex] is found by subtracting [tex]\(g(2)\)[/tex] from [tex]\(f(2)\)[/tex]:
[tex]\[ (f - g)(2) = f(2) - g(2) \][/tex]
Substitute the values we calculated:
[tex]\[ (f - g)(2) = 13 - (-1) \][/tex]
This simplifies to:
[tex]\[ 13 + 1 = 14 \][/tex]
So, the value of [tex]\((f - g)(2)\)[/tex] is [tex]\(\boxed{14}\)[/tex].
1. Evaluate [tex]\(f(x)\)[/tex] at [tex]\(x = 2\)[/tex]:
Recall the function [tex]\(f(x) = 3x^2 + 1\)[/tex].
Plug in [tex]\(x = 2\)[/tex]:
[tex]\[ f(2) = 3(2)^2 + 1 \][/tex]
Calculate the square of 2:
[tex]\[ (2)^2 = 4 \][/tex]
Multiply by 3:
[tex]\[ 3 \times 4 = 12 \][/tex]
Add 1:
[tex]\[ 12 + 1 = 13 \][/tex]
Therefore,
[tex]\[ f(2) = 13 \][/tex]
2. Evaluate [tex]\(g(x)\)[/tex] at [tex]\(x = 2\)[/tex]:
Recall the function [tex]\(g(x) = 1 - x\)[/tex].
Plug in [tex]\(x = 2\)[/tex]:
[tex]\[ g(2) = 1 - 2 \][/tex]
Subtract 2 from 1:
[tex]\[ 1 - 2 = -1 \][/tex]
Therefore,
[tex]\[ g(2) = -1 \][/tex]
3. Combine the results to find [tex]\((f - g)(2)\)[/tex]:
The expression [tex]\((f - g)(2)\)[/tex] is found by subtracting [tex]\(g(2)\)[/tex] from [tex]\(f(2)\)[/tex]:
[tex]\[ (f - g)(2) = f(2) - g(2) \][/tex]
Substitute the values we calculated:
[tex]\[ (f - g)(2) = 13 - (-1) \][/tex]
This simplifies to:
[tex]\[ 13 + 1 = 14 \][/tex]
So, the value of [tex]\((f - g)(2)\)[/tex] is [tex]\(\boxed{14}\)[/tex].